Most of my engine failures have been with that engine model!
I suspect that the failure on closing the throttle is probably down to tickover being set too low - I've seen that a couple of times test flying homebuilts, and it may be unrelated to the other issues.
J2.2s can ice, and there are various carb heat solutions available. Not all of them are brilliant, hence that I've seen several aeroplanes with multiple carb heat systems. I would take a look at that, and see if you're truly satisfied that it's up to the job.
What state were the plugs, before and after?
I'm not sure I've ever seen a mixture control for a Jabiru.
G